MATHEMATICS HIGH SCHOOL

Which strategie would eliminate a variable in the system of equations? −x+6y=8 7x−y=−2 ​

Answers

Answer 1
Answer:

Answer:

  substitution (or addition)

Step-by-step explanation:

A simple strategy for this system is to use substitution. The first equation is easily solved for x, so you could substitute that into the second equation:

  x = 6y -8

  7(6y -8) -y = -2 . . . . . x variable eliminated

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The second equation is easily solved for y, so you could substitute that into the first equation.

  y = 7x +2

  -x +6(7x +2) = 8 . . . . . y-variable eliminated

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The "addition" method is always a good way to eliminate a variable.

When the coefficient of a variable in one equation is a divisor of the coefficient of that variable in the other equation, a simple multiplication and addition will do.

To make the coefficient of x in the first equation the opposite of the coefficient of x in the second, multiply the first equation by 7. Adding that result to the second equation will eliminate x:

   7(-x +6y) +(7x -y) = 7(8) +(-2)

  42y -y = 56 -2 . . . . . . x-variable eliminated

Likewise, the second equation can be multiplied by 6 and added to the first to eliminate the y-variable:

  (-x +6y) +6(7x -y) = (8) +6(-2)

  -x +42x = -4 . . . . . . . . y-variable eliminated

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It is often the case that using either substitution or "addition" requires about the same amount of work.

Here, the solutions are (x, y) = (-4/41, 54/41).
Answer 2
Answer:

Final answer:

To eliminate a variable in the given system of equations, you can use the elimination method. By multiplying the equations by suitable numbers and adding them, you can cancel out one of the variables, simplifying the process to solve for the other variable.

Explanation:

You can eliminate a variable in the given system of equations: −x+6y=8 and 7x-y=−2 by using either the substitution method or the elimination method. For this scenario, the elimination method will work best.

Strategy:

  1. To eliminate x, you should first multiply the first equation by 7 and the second by 1, resulting in the equations: -7x+42y=56 and 7x-y=-2
  2. Adding these two equations together, the x terms (-7x and 7x) cancel out, giving us: 41y=54.
  3. Finally, you divide both sides by 41 to solve for y. This process effectively eliminates the variable x from the equation, providing a solution for y.

This variable eliminationstrategy lets you solve one equation for one variable, simplifying the process of finding solutions for a system of equations.

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For each hour he babysits, Anderson earns $1 more than half of Carey’s hourly rate. Anderson earns $6 per hour. Which equation can be used to solve for Carey’s hourly rate, c?

Answers

Carey earns c hourly
Anderson earns $6 hourly which is also 1+ c/2
So, 6=1+c/2
      12=2+c
c=$10
Carey earns $10 hourly
For each hour he babysits, Anderson earns $1 more than half of Carey’s hourly rate. Anderson earns $6 per hour.
6 = c/2 + 1
5 = c/2
10 = c

Natalie buys organic almonds priced at $77 from the grocery store. How much did she pay the cashier if she received $23 in change?

Answers

She paid $100 because she bought the almonds for $77 then she received $23 back (100-77=23) (77+23=100)

Find 3 consecutive numbers where the product of the smaller two numbers in 19 less than the square of the largest number?

Answers

Answer is 5, 6, & 7

x = smallest number
y = x + 1
z = x + 2

(x)(y) = z^2 - 19
(x)(x+1) = (x + 2)^2 - 19
(x^2 + x) = (x^2 + 4x + 4) - 19
x^2 + x = x^2 + 4x + 4 - 19

x^2 term drops out from both sides

x = 4x + -15
15 = 4x - x
15 = 3x
15/3 = x
x = 5
y = x + 1 = 6
z = x + 2 = 7

Confirm by substituting back in for the variables:
(x)(y) = z^2 - 19
(5)(6) = (7)^2 - 19
30 = 49 - 19
30 = 30  [OK]

Write 2.11111... as a fraction.

Answers

Answer:

19/9

Step-by-step explanation:

x=2.1 repeating

10x=21.1 repeating

subtract x from 10x and you get 9x=19

divide by 9 on both sides of the equal sign to get x=19/9

how much material was used in the manufacture of 24000 celluloid dice,if each dice has an edge 1/4 inches?

Answers

The volume of each celluloid die is (.25 x .25 x .25) = 0.015625 cubic inch.

To manufacture 24,000 of them, you need to start with at least

(24,000) x (0.015625) = 375 cubic inches.

I don't know how celluloid is sold, so you should also keep in mind that
375 cubic inches = about 207.8 fluid ounces, or about 6.5 quarts.

I'm sure a bit more than that was used in the manufacture, since
there's always some wasted, spilled, or trimmed off of the edges.

Pedro works as a newspaper deliverer. He receives a base pay plus an additional amount per newspaper delivered. Last week, Pedro delivered 5 newspapers and earned $37.50. This week, he delivered 20 newspapers and earned $75. Let x equal the number of newspapers Pedro delivers and y be the earnings he receives in dollars. Which linear function models the scenario?

Answers

y=mx+b
x=number of newspapers
37.5 earned for 5 newspapers
37.5=5m+b

earned 75 and deliverd 20 newpapers
75=20m+b

we have

37.5=5m+b and
75=20m+b
multiply first equaiton by -1 and add to other equaiton

-37.5=-5m-b
75=20m+b  +
37.5=15m+0b

37.5=15m
divide both sides by 15
2.5=m

sub back to find b
75=2.5(20)+b
75=50+b
minsu 50 both sides
25=b

y=2.5x+25 is lnear funtion

The linearfunction is y=2.5x+25

What is linear function?

A linear function is a function whose graph is a straightline, that is, a polynomial function of degreezero or one.

As, we know equation of line

y=mx + b

x=number of newspapers

37.5=5m+b...............(1)

also,

75=20m+b....................(2)

Solving (1) and (2) , we get

37.5=15m

m=2.5

and, 75=2.5(20)+b

75=50+b

b= 25

Hence, y=2.5x+25 is linear function.

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